Bayesian Dose-Finding Trial Simulation

Introduction

This document provides an interactive way to run the Bayesian dose-finding trial simulation. You can modify the simulation parameters in the “Configuration” section and then run the code chunks to see the results.

Setup

This chunk loads the necessary libraries and source files.

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library(knitr) # For creating formatted tables
library(ggplot2)

# Set working directory to project root for consistent paths
if (basename(getwd()) == "notebooks") {
  setwd("..")
}

source("src/core/config.R")

=======

library(knitr)
library(ggplot2)

# Use absolute paths
project_root <- "/Users/jz/Development/DoseFinding"
cat("Project root:", project_root, "\n")

Project root: /Users/jz/Development/DoseFinding 

# Source core files
source(file.path(project_root, "src/core/config.R"))

>>>>>>> origin/main

Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

Iso 0.0-21

     An "infelicity" in the function ufit() (whereby 
     it was all too easy to conflate the location of 
     the mode with its index in the entries of the 
     "x" argument) has been corrected.  To this end, 
     ufit() now has arguments "lmode" (the location 
     of the mode), and "imode" (its index).  At most 
     one of these arguments should be specified.  See 
     the help for ufit().

<<<<<<< HEAD

source("src/utils/helpers.R")
source("src/utils/plotting_extensions.R")
source("src/core/simulate_data.R")
source("src/core/model_utils.R")
source("src/decision/dose_decision.R")
source("src/core/main.R")

=======

source(file.path(project_root, "src/utils/helpers.R"))
source(file.path(project_root, "src/utils/plotting_extensions.R"))
source(file.path(project_root, "src/core/simulate_data.R"))
source(file.path(project_root, "src/core/model_utils.R"))
source(file.path(project_root, "src/decision/dose_decision.R"))
source(file.path(project_root, "src/core/main.R"))

>>>>>>> origin/main

Configuration

Modify the simulation parameters in this section. I have adjusted these values to create a more dynamic scenario where multiple doses are likely to be admissible in the early stages.

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Calibration Note: The c_poc parameter has been calibrated using null/flat scenarios to control Type I error at approximately 10%. The optimal value of c_poc = 0.95 achieves a 7.8% false positive rate. For stricter Type I error control matching the calibration conditions, consider using the threshold configuration from poc_calibration_notebook.qmd (phi_T=0.3, c_T=0.3, phi_E=0.25, c_E=0.3).

# Trial configuration
# Note: These parameters allow for interactive exploration with different scenarios.
# For calibrated Type I error control (~10%), use the stricter thresholds from 
# poc_calibration_notebook.qmd: phi_T=0.3, c_T=0.3, phi_E=0.25, c_E=0.3, phi_I=0.2, c_I=0.2

trial_config <- list(
  dose_levels = c(1, 2, 3, 4, 5),
  n_stages = 5,
  cohort_size = 15,
  phi_T = 0.35, # Toxicity threshold (relaxed for exploration)
  c_T = 0.5,   
  phi_E = 0.1, # Efficacy threshold (relaxed for exploration)
  c_E = 0.5,   
  phi_I = 0.20, # Immune response threshold
  c_I = 0.5,   
  # PoC parameters (calibrated value from null/flat scenario testing)
  c_poc = 0.95,  # Calibrated to achieve ~7.8% Type I error (target ≤10%)
  delta_poc = 0.8,  # Threshold for PoC pairwise comparison
  # Early termination parameters
  enable_early_termination = TRUE,
  log_early_termination = TRUE
)
#cohort size may vary on diff stage (future work)

# Data simulation parameters (designed for a more interesting trial)
p_YI <- c(0.10, 0.30, 0.50, 0.60, 0.70) # Immune response probability

p_YT_given_I <- matrix(c(
  # I=0 (No Immune Response)
  0.05, 0.10, 0.12, 0.18, 0.25,
  # I=1 (Immune Response)
  0.08, 0.12, 0.15, 0.25, 0.35
), nrow = 5, ncol = 2)

p_YE_given_I <- matrix(c(
  # I=0 (No Immune Response)
  0.10, 0.20, 0.35, 0.45, 0.50, 
  # I=1 (Immune Response)
  0.30, 0.50, 0.70, 0.80, 0.75  
), nrow = 5, ncol = 2)

rho0 <- 1.5
rho1 <- 2

# Utility table
# Rows: Efficacy (0, 1)
# Columns: Toxicity (0, 1)
# Slices: Immune Response (0, 1)
utility_table <- array(0, dim = c(2, 2, 2), dimnames = list(
  E = c(0, 1),
  T = c(0, 1),
  I = c(0, 1)
))

utility_table[1, 1, 1] <- 0   # E=0, T=0, I=0
utility_table[2, 1, 1] <- 80  # E=1, T=0, I=0
utility_table[1, 2, 1] <- 0   # E=0, T=1, I=0
utility_table[2, 2, 1] <- 30  # E=1, T=1, I=0

utility_table[1, 1, 2] <- 10  # E=0, T=0, I=1
utility_table[2, 1, 2] <- 100 # E=1, T=0, I=1
utility_table[1, 2, 2] <- 0   # E=0, T=1, I=1
utility_table[2, 2, 2] <- 40  # E=1, T=1, I=1

trial_config$utility_table <- utility_table

=======

# Trial configuration
trial_config <- list(
  dose_levels = c(1, 2, 3, 4, 5),
  n_stages = 5,
  cohort_size = 15,
  phi_T = 0.35, # Toxicity threshold (increased slightly)
  c_T = 0.5,   
  phi_E = 0.1, # Efficacy threshold (increased slightly)
  c_E = 0.5,   
  phi_I = 0.20, # Immune response threshold
  c_I = 0.5,   
  # PoC parameters
  c_poc = 0.9,
  delta_poc = 0.8,  # Threshold for PoC comparison
  # Early termination parameters
  enable_early_termination = TRUE,
  log_early_termination = TRUE
)
#cohort size may vary on diff stage (future work)

# Data simulation parameters (designed for a more interesting trial)
p_YI <- c(0.10, 0.30, 0.50, 0.60, 0.70) # Immune response probability

p_YT_given_I <- matrix(c(
  # I=0 (No Immune Response)
  0.05, 0.10, 0.12, 0.18, 0.25,
  # I=1 (Immune Response)
  0.08, 0.12, 0.15, 0.25, 0.35
), nrow = 5, ncol = 2)

p_YE_given_I <- matrix(c(
  # I=0 (No Immune Response)
  0.10, 0.20, 0.35, 0.45, 0.50, 
  # I=1 (Immune Response)
  0.30, 0.50, 0.70, 0.80, 0.75  
), nrow = 5, ncol = 2)

rho0 <- 1.5
rho1 <- 2

# Utility table
# Rows: Efficacy (0, 1)
# Columns: Toxicity (0, 1)
# Slices: Immune Response (0, 1)
utility_table <- array(0, dim = c(2, 2, 2), dimnames = list(
  E = c(0, 1),
  T = c(0, 1),
  I = c(0, 1)
))

utility_table[1, 1, 1] <- 0   # E=0, T=0, I=0
utility_table[2, 1, 1] <- 80  # E=1, T=0, I=0
utility_table[1, 2, 1] <- 0   # E=0, T=1, I=0
utility_table[2, 2, 1] <- 30  # E=1, T=1, I=0

utility_table[1, 1, 2] <- 10  # E=0, T=0, I=1
utility_table[2, 1, 2] <- 100 # E=1, T=0, I=1
utility_table[1, 2, 2] <- 0   # E=0, T=1, I=1
utility_table[2, 2, 2] <- 40  # E=1, T=1, I=1

trial_config$utility_table <- utility_table

>>>>>>> origin/main

Simulation

<<<<<<< HEAD

This chunk runs the multi-stage trial simulation by calling the run_trial_simulation function. The simulation follows the workflow specified in TRIAL_DESIGN.md Section 7.1:

1. Stage 1: Equal randomization to all dose levels
2. Interim Analysis: Update admissible set based on posterior probabilities
3. Early Termination Check: Terminate if admissible set is empty (checked after interim analysis, before adaptive randomization)
4. Adaptive Randomization: Allocate patients based on utility scores (Stages 2+ only, only if trial continues)
5. Final Selection: Choose OD with highest utility from admissible set + PoC validation

results <- run_trial_simulation(trial_config, p_YI, p_YT_given_I, p_YE_given_I, rho0, rho1)

--- Stage 1 ---
Workflow: Step 1 - Equal randomization to all dose levels
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.252 0.286 0.371 0.551 0.644 
Summary: Efficacy marginal means: 0.171 0.256 0.358 0.522 0.687 
Summary: Immune response means: 0.158 0.239 0.531 0.604 0.684 
Dose 1 : P(Tox <  0.35 ) =  0.84 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.76 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.31 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  0.75 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.96 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.55 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  0.44 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.99 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  0.04 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
=======
This chunk runs the multi-stage trial simulation by calling the run_trial_simulation function. The simulation follows the workflow specified in TRIAL_DESIGN.md:

Stage 1: Equal randomization to all dose levels
Interim Analysis: Update admissible set based on posterior probabilities
Adaptive Randomization: Allocate patients based on utility scores
Early Termination Check: Terminate if admissible set is empty
Final Selection: Choose OD with highest utility from admissible set + PoC validation


results <- run_trial_simulation(trial_config, p_YI, p_YT_given_I, p_YE_given_I, rho0, rho1)


--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.238 0.272 0.338 0.358 0.412 
Summary: Efficacy marginal means: 0.321 0.41 0.468 0.55 0.782 
Summary: Immune response means: 0.159 0.24 0.479 0.517 0.81 
Dose 1 : P(Tox <  0.35 ) =  0.9 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.97 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.33 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  0.82 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.56 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  0.58 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.99 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  0.47 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.99 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.159 
  Toxicity given I=0 (π_T|I=0): 0.22 
  Toxicity given I=1 (π_T|I=1): 0.34 
  Efficacy given I=0 (π_E|I=0): 0.3 
  Efficacy given I=1 (π_E|I=1): 0.43 
  Probability distributions:
    P(T=0|I=0): 0.78 P(T=1|I=0): 0.22 
    P(T=0|I=1): 0.66 P(T=1|I=1): 0.34 
    P(E=0|I=0): 0.7 P(E=1|I=0): 0.3 
    P(E=0|I=1): 0.57 P(E=1|I=1): 0.43 
  Expected utility given I=0: 20.69 
  Expected utility given I=1: 37.97 
  Total expected utility: 23.43 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.24 
  Toxicity given I=0 (π_T|I=0): 0.238 
  Toxicity given I=1 (π_T|I=1): 0.379 
  Efficacy given I=0 (π_E|I=0): 0.382 
  Efficacy given I=1 (π_E|I=1): 0.501 
  Probability distributions:
    P(T=0|I=0): 0.762 P(T=1|I=0): 0.238 
    P(T=0|I=1): 0.621 P(T=1|I=1): 0.379 
    P(E=0|I=0): 0.618 P(E=1|I=0): 0.382 
    P(E=0|I=1): 0.499 P(E=1|I=1): 0.501 
  Expected utility given I=0: 26.04 
  Expected utility given I=1: 41.85 
  Total expected utility: 29.84 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.479 
  Toxicity given I=0 (π_T|I=0): 0.282 
  Toxicity given I=1 (π_T|I=1): 0.398 
  Efficacy given I=0 (π_E|I=0): 0.387 
  Efficacy given I=1 (π_E|I=1): 0.556 
  Probability distributions:
    P(T=0|I=0): 0.718 P(T=1|I=0): 0.282 
    P(T=0|I=1): 0.602 P(T=1|I=1): 0.398 
    P(E=0|I=0): 0.613 P(E=1|I=0): 0.387 
    P(E=0|I=1): 0.444 P(E=1|I=1): 0.556 
  Expected utility given I=0: 25.51 
  Expected utility given I=1: 45 
  Total expected utility: 34.85 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.517 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.404 
  Efficacy given I=0 (π_E|I=0): 0.403 
  Efficacy given I=1 (π_E|I=1): 0.689 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.596 P(T=1|I=1): 0.404 
    P(E=0|I=0): 0.597 P(E=1|I=0): 0.403 
    P(E=0|I=1): 0.311 P(E=1|I=1): 0.689 
  Expected utility given I=0: 26.01 
  Expected utility given I=1: 54.04 
  Total expected utility: 40.49 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.81 
  Toxicity given I=0 (π_T|I=0): 0.377 
  Toxicity given I=1 (π_T|I=1): 0.42 
  Efficacy given I=0 (π_E|I=0): 0.56 
  Efficacy given I=1 (π_E|I=1): 0.835 
  Probability distributions:
    P(T=0|I=0): 0.623 P(T=1|I=0): 0.377 
    P(T=0|I=1): 0.58 P(T=1|I=1): 0.42 
    P(E=0|I=0): 0.44 P(E=1|I=0): 0.56 
    P(E=0|I=1): 0.165 P(E=1|I=1): 0.835 
  Expected utility given I=0: 34.24 
  Expected utility given I=1: 63.45 
  Total expected utility: 57.89 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.159 |    0.220 |    0.340 |    0.300 |    0.430 |   20.7 |   38.0 |    23.4
   2 |  0.240 |    0.238 |    0.379 |    0.382 |    0.501 |   26.0 |   41.8 |    29.8
   3 |  0.479 |    0.282 |    0.398 |    0.387 |    0.556 |   25.5 |   45.0 |    34.8
   4 |  0.517 |    0.309 |    0.404 |    0.403 |    0.689 |   26.0 |   54.0 |    40.5
   5 |  0.810 |    0.377 |    0.420 |    0.560 |    0.835 |   34.2 |   63.5 |    57.9

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.4612858 0.5387142 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.147 0.17 0.258 0.308 0.375 
Summary: Efficacy marginal means: 0.289 0.345 0.406 0.535 0.774 
Summary: Immune response means: 0.158 0.272 0.544 0.564 0.815 
Dose 1 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.97 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.32 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.71 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  0.91 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.48 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 4 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.158 
  Toxicity given I=0 (π_T|I=0): 0.126 
  Toxicity given I=1 (π_T|I=1): 0.258 
  Efficacy given I=0 (π_E|I=0): 0.278 
  Efficacy given I=1 (π_E|I=1): 0.35 
  Probability distributions:
    P(T=0|I=0): 0.874 P(T=1|I=0): 0.126 
    P(T=0|I=1): 0.742 P(T=1|I=1): 0.258 
    P(E=0|I=0): 0.722 P(E=1|I=0): 0.278 
    P(E=0|I=1): 0.65 P(E=1|I=1): 0.35 
  Expected utility given I=0: 20.48 
  Expected utility given I=1: 34.44 
  Total expected utility: 22.69 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.272 
  Toxicity given I=0 (π_T|I=0): 0.13 
  Toxicity given I=1 (π_T|I=1): 0.277 
  Efficacy given I=0 (π_E|I=0): 0.332 
  Efficacy given I=1 (π_E|I=1): 0.382 
  Probability distributions:
    P(T=0|I=0): 0.87 P(T=1|I=0): 0.13 
    P(T=0|I=1): 0.723 P(T=1|I=1): 0.277 
    P(E=0|I=0): 0.668 P(E=1|I=0): 0.332 
    P(E=0|I=1): 0.618 P(E=1|I=1): 0.382 
  Expected utility given I=0: 24.37 
  Expected utility given I=1: 36.3 
  Total expected utility: 27.62 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.544 
  Toxicity given I=0 (π_T|I=0): 0.179 
  Toxicity given I=1 (π_T|I=1): 0.323 
  Efficacy given I=0 (π_E|I=0): 0.333 
  Efficacy given I=1 (π_E|I=1): 0.467 
  Probability distributions:
    P(T=0|I=0): 0.821 P(T=1|I=0): 0.179 
    P(T=0|I=1): 0.677 P(T=1|I=1): 0.323 
    P(E=0|I=0): 0.667 P(E=1|I=0): 0.333 
    P(E=0|I=1): 0.533 P(E=1|I=1): 0.467 
  Expected utility given I=0: 23.63 
  Expected utility given I=1: 41.24 
  Total expected utility: 33.2 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.564 
  Toxicity given I=0 (π_T|I=0): 0.248 
  Toxicity given I=1 (π_T|I=1): 0.355 
  Efficacy given I=0 (π_E|I=0): 0.364 
  Efficacy given I=1 (π_E|I=1): 0.669 
  Probability distributions:
    P(T=0|I=0): 0.752 P(T=1|I=0): 0.248 
    P(T=0|I=1): 0.645 P(T=1|I=1): 0.355 
    P(E=0|I=0): 0.636 P(E=1|I=0): 0.364 
    P(E=0|I=1): 0.331 P(E=1|I=1): 0.669 
  Expected utility given I=0: 24.6 
  Expected utility given I=1: 54.79 
  Total expected utility: 41.62 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.815 
  Toxicity given I=0 (π_T|I=0): 0.343 
  Toxicity given I=1 (π_T|I=1): 0.382 
  Efficacy given I=0 (π_E|I=0): 0.551 
  Efficacy given I=1 (π_E|I=1): 0.825 
  Probability distributions:
    P(T=0|I=0): 0.657 P(T=1|I=0): 0.343 
    P(T=0|I=1): 0.618 P(T=1|I=1): 0.382 
    P(E=0|I=0): 0.449 P(E=1|I=0): 0.551 
    P(E=0|I=1): 0.175 P(E=1|I=1): 0.825 
  Expected utility given I=0: 34.6 
  Expected utility given I=1: 64.65 
  Total expected utility: 59.09 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.158 |    0.126 |    0.258 |    0.278 |    0.350 |   20.5 |   34.4 |    22.7
   2 |  0.272 |    0.130 |    0.277 |    0.332 |    0.382 |   24.4 |   36.3 |    27.6
   3 |  0.544 |    0.179 |    0.323 |    0.333 |    0.467 |   23.6 |   41.2 |    33.2
   4 |  0.564 |    0.248 |    0.355 |    0.364 |    0.669 |   24.6 |   54.8 |    41.6
   5 |  0.815 |    0.343 |    0.382 |    0.551 |    0.825 |   34.6 |   64.6 |    59.1

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.2695908 0.3241299 0.4062793 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.124 0.14 0.203 0.224 0.333 
Summary: Efficacy marginal means: 0.304 0.373 0.449 0.528 0.768 
Summary: Immune response means: 0.178 0.321 0.51 0.517 0.809 
Dose 1 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.97 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.4 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  0.96 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.62 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 4 5 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.178 
  Toxicity given I=0 (π_T|I=0): 0.11 
  Toxicity given I=1 (π_T|I=1): 0.19 
  Efficacy given I=0 (π_E|I=0): 0.294 
  Efficacy given I=1 (π_E|I=1): 0.349 
  Probability distributions:
    P(T=0|I=0): 0.89 P(T=1|I=0): 0.11 
    P(T=0|I=1): 0.81 P(T=1|I=1): 0.19 
    P(E=0|I=0): 0.706 P(E=1|I=0): 0.294 
    P(E=0|I=1): 0.651 P(E=1|I=1): 0.349 
  Expected utility given I=0: 21.9 
  Expected utility given I=1: 36.14 
  Total expected utility: 24.43 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.321 
  Toxicity given I=0 (π_T|I=0): 0.112 
  Toxicity given I=1 (π_T|I=1): 0.202 
  Efficacy given I=0 (π_E|I=0): 0.371 
  Efficacy given I=1 (π_E|I=1): 0.379 
  Probability distributions:
    P(T=0|I=0): 0.888 P(T=1|I=0): 0.112 
    P(T=0|I=1): 0.798 P(T=1|I=1): 0.202 
    P(E=0|I=0): 0.629 P(E=1|I=0): 0.371 
    P(E=0|I=1): 0.621 P(E=1|I=1): 0.379 
  Expected utility given I=0: 27.59 
  Expected utility given I=1: 38.24 
  Total expected utility: 31.01 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.51 
  Toxicity given I=0 (π_T|I=0): 0.162 
  Toxicity given I=1 (π_T|I=1): 0.242 
  Efficacy given I=0 (π_E|I=0): 0.392 
  Efficacy given I=1 (π_E|I=1): 0.503 
  Probability distributions:
    P(T=0|I=0): 0.838 P(T=1|I=0): 0.162 
    P(T=0|I=1): 0.758 P(T=1|I=1): 0.242 
    P(E=0|I=0): 0.608 P(E=1|I=0): 0.392 
    P(E=0|I=1): 0.497 P(E=1|I=1): 0.503 
  Expected utility given I=0: 28.15 
  Expected utility given I=1: 46.75 
  Total expected utility: 37.64 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.517 
  Toxicity given I=0 (π_T|I=0): 0.178 
  Toxicity given I=1 (π_T|I=1): 0.266 
  Efficacy given I=0 (π_E|I=0): 0.427 
  Efficacy given I=1 (π_E|I=1): 0.623 
  Probability distributions:
    P(T=0|I=0): 0.822 P(T=1|I=0): 0.178 
    P(T=0|I=1): 0.734 P(T=1|I=1): 0.266 
    P(E=0|I=0): 0.573 P(E=1|I=0): 0.427 
    P(E=0|I=1): 0.377 P(E=1|I=1): 0.623 
  Expected utility given I=0: 30.33 
  Expected utility given I=1: 55.14 
  Total expected utility: 43.15 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.809 
  Toxicity given I=0 (π_T|I=0): 0.302 
  Toxicity given I=1 (π_T|I=1): 0.339 
  Efficacy given I=0 (π_E|I=0): 0.564 
  Efficacy given I=1 (π_E|I=1): 0.818 
  Probability distributions:
    P(T=0|I=0): 0.698 P(T=1|I=0): 0.302 
    P(T=0|I=1): 0.661 P(T=1|I=1): 0.339 
    P(E=0|I=0): 0.436 P(E=1|I=0): 0.564 
    P(E=0|I=1): 0.182 P(E=1|I=1): 0.818 
  Expected utility given I=0: 36.63 
  Expected utility given I=1: 66.34 
  Total expected utility: 60.66 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.178 |    0.110 |    0.190 |    0.294 |    0.349 |   21.9 |   36.1 |    24.4
   2 |  0.321 |    0.112 |    0.202 |    0.371 |    0.379 |   27.6 |   38.2 |    31.0
   3 |  0.510 |    0.162 |    0.242 |    0.392 |    0.503 |   28.2 |   46.8 |    37.6
   4 |  0.517 |    0.178 |    0.266 |    0.427 |    0.623 |   30.3 |   55.1 |    43.1
   5 |  0.809 |    0.302 |    0.339 |    0.564 |    0.818 |   36.6 |   66.3 |    60.7

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.1798065 0.2182409 0.2501857 0.3517669 

--- Stage 4 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.105 0.119 0.178 0.189 0.235 
Summary: Efficacy marginal means: 0.286 0.337 0.471 0.534 0.801 
Summary: Immune response means: 0.177 0.324 0.525 0.526 0.799 
Dose 1 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.97 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.41 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.89 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 4 5 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.177 
  Toxicity given I=0 (π_T|I=0): 0.092 
  Toxicity given I=1 (π_T|I=1): 0.166 
  Efficacy given I=0 (π_E|I=0): 0.278 
  Efficacy given I=1 (π_E|I=1): 0.325 
  Probability distributions:
    P(T=0|I=0): 0.908 P(T=1|I=0): 0.092 
    P(T=0|I=1): 0.834 P(T=1|I=1): 0.166 
    P(E=0|I=0): 0.722 P(E=1|I=0): 0.278 
    P(E=0|I=1): 0.675 P(E=1|I=1): 0.325 
  Expected utility given I=0: 20.93 
  Expected utility given I=1: 34.9 
  Total expected utility: 23.4 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.324 
  Toxicity given I=0 (π_T|I=0): 0.093 
  Toxicity given I=1 (π_T|I=1): 0.175 
  Efficacy given I=0 (π_E|I=0): 0.335 
  Efficacy given I=1 (π_E|I=1): 0.343 
  Probability distributions:
    P(T=0|I=0): 0.907 P(T=1|I=0): 0.093 
    P(T=0|I=1): 0.825 P(T=1|I=1): 0.175 
    P(E=0|I=0): 0.665 P(E=1|I=0): 0.335 
    P(E=0|I=1): 0.657 P(E=1|I=1): 0.343 
  Expected utility given I=0: 25.21 
  Expected utility given I=1: 36.16 
  Total expected utility: 28.76 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.525 
  Toxicity given I=0 (π_T|I=0): 0.131 
  Toxicity given I=1 (π_T|I=1): 0.221 
  Efficacy given I=0 (π_E|I=0): 0.349 
  Efficacy given I=1 (π_E|I=1): 0.581 
  Probability distributions:
    P(T=0|I=0): 0.869 P(T=1|I=0): 0.131 
    P(T=0|I=1): 0.779 P(T=1|I=1): 0.221 
    P(E=0|I=0): 0.651 P(E=1|I=0): 0.349 
    P(E=0|I=1): 0.419 P(E=1|I=1): 0.581 
  Expected utility given I=0: 25.67 
  Expected utility given I=1: 53.67 
  Total expected utility: 40.36 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.526 
  Toxicity given I=0 (π_T|I=0): 0.139 
  Toxicity given I=1 (π_T|I=1): 0.235 
  Efficacy given I=0 (π_E|I=0): 0.359 
  Efficacy given I=1 (π_E|I=1): 0.691 
  Probability distributions:
    P(T=0|I=0): 0.861 P(T=1|I=0): 0.139 
    P(T=0|I=1): 0.765 P(T=1|I=1): 0.235 
    P(E=0|I=0): 0.641 P(E=1|I=0): 0.359 
    P(E=0|I=1): 0.309 P(E=1|I=1): 0.691 
  Expected utility given I=0: 26.23 
  Expected utility given I=1: 61.74 
  Total expected utility: 44.9 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.799 
  Toxicity given I=0 (π_T|I=0): 0.205 
  Toxicity given I=1 (π_T|I=1): 0.242 
  Efficacy given I=0 (π_E|I=0): 0.442 
  Efficacy given I=1 (π_E|I=1): 0.891 
  Probability distributions:
    P(T=0|I=0): 0.795 P(T=1|I=0): 0.205 
    P(T=0|I=1): 0.758 P(T=1|I=1): 0.242 
    P(E=0|I=0): 0.558 P(E=1|I=0): 0.442 
    P(E=0|I=1): 0.109 P(E=1|I=1): 0.891 
  Expected utility given I=0: 30.8 
  Expected utility given I=1: 76.98 
  Total expected utility: 67.69 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.177 |    0.092 |    0.166 |    0.278 |    0.325 |   20.9 |   34.9 |    23.4
   2 |  0.324 |    0.093 |    0.175 |    0.335 |    0.343 |   25.2 |   36.2 |    28.8
   3 |  0.525 |    0.131 |    0.221 |    0.349 |    0.581 |   25.7 |   53.7 |    40.4
   4 |  0.526 |    0.139 |    0.235 |    0.359 |    0.691 |   26.2 |   61.7 |    44.9
   5 |  0.799 |    0.205 |    0.242 |    0.442 |    0.891 |   30.8 |   77.0 |    67.7

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.1582726 0.2221118 0.2471072 0.3725084 

--- Stage 5 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.092 0.107 0.163 0.177 0.219 
Summary: Efficacy marginal means: 0.277 0.319 0.491 0.556 0.745 
Summary: Immune response means: 0.173 0.343 0.533 0.534 0.641 
Dose 1 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.97 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.39 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.94 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.96 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 4 5 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.173 
  Toxicity given I=0 (π_T|I=0): 0.08 
  Toxicity given I=1 (π_T|I=1): 0.15 
  Efficacy given I=0 (π_E|I=0): 0.27 
  Efficacy given I=1 (π_E|I=1): 0.306 
  Probability distributions:
    P(T=0|I=0): 0.92 P(T=1|I=0): 0.08 
    P(T=0|I=1): 0.85 P(T=1|I=1): 0.15 
    P(E=0|I=0): 0.73 P(E=1|I=0): 0.27 
    P(E=0|I=1): 0.694 P(E=1|I=1): 0.306 
  Expected utility given I=0: 20.51 
  Expected utility given I=1: 33.78 
  Total expected utility: 22.8 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.343 
  Toxicity given I=0 (π_T|I=0): 0.081 
  Toxicity given I=1 (π_T|I=1): 0.157 
  Efficacy given I=0 (π_E|I=0): 0.318 
  Efficacy given I=1 (π_E|I=1): 0.322 
  Probability distributions:
    P(T=0|I=0): 0.919 P(T=1|I=0): 0.081 
    P(T=0|I=1): 0.843 P(T=1|I=1): 0.157 
    P(E=0|I=0): 0.682 P(E=1|I=0): 0.318 
    P(E=0|I=1): 0.678 P(E=1|I=1): 0.322 
  Expected utility given I=0: 24.15 
  Expected utility given I=1: 34.88 
  Total expected utility: 27.83 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.533 
  Toxicity given I=0 (π_T|I=0): 0.114 
  Toxicity given I=1 (π_T|I=1): 0.205 
  Efficacy given I=0 (π_E|I=0): 0.327 
  Efficacy given I=1 (π_E|I=1): 0.634 
  Probability distributions:
    P(T=0|I=0): 0.886 P(T=1|I=0): 0.114 
    P(T=0|I=1): 0.795 P(T=1|I=1): 0.205 
    P(E=0|I=0): 0.673 P(E=1|I=0): 0.327 
    P(E=0|I=1): 0.366 P(E=1|I=1): 0.634 
  Expected utility given I=0: 24.33 
  Expected utility given I=1: 58.52 
  Total expected utility: 42.55 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.534 
  Toxicity given I=0 (π_T|I=0): 0.119 
  Toxicity given I=1 (π_T|I=1): 0.228 
  Efficacy given I=0 (π_E|I=0): 0.336 
  Efficacy given I=1 (π_E|I=1): 0.747 
  Probability distributions:
    P(T=0|I=0): 0.881 P(T=1|I=0): 0.119 
    P(T=0|I=1): 0.772 P(T=1|I=1): 0.228 
    P(E=0|I=0): 0.664 P(E=1|I=0): 0.336 
    P(E=0|I=1): 0.253 P(E=1|I=1): 0.747 
  Expected utility given I=0: 24.89 
  Expected utility given I=1: 66.41 
  Total expected utility: 47.06 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.641 
  Toxicity given I=0 (π_T|I=0): 0.201 
  Toxicity given I=1 (π_T|I=1): 0.229 
  Efficacy given I=0 (π_E|I=0): 0.576 
  Efficacy given I=1 (π_E|I=1): 0.84 
  Probability distributions:
    P(T=0|I=0): 0.799 P(T=1|I=0): 0.201 
    P(T=0|I=1): 0.771 P(T=1|I=1): 0.229 
    P(E=0|I=0): 0.424 P(E=1|I=0): 0.576 
    P(E=0|I=1): 0.16 P(E=1|I=1): 0.84 
  Expected utility given I=0: 40.29 
  Expected utility given I=1: 73.67 
  Total expected utility: 61.69 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.173 |    0.080 |    0.150 |    0.270 |    0.306 |   20.5 |   33.8 |    22.8
   2 |  0.343 |    0.081 |    0.157 |    0.318 |    0.322 |   24.2 |   34.9 |    27.8
   3 |  0.533 |    0.114 |    0.205 |    0.327 |    0.634 |   24.3 |   58.5 |    42.5
   4 |  0.534 |    0.119 |    0.228 |    0.336 |    0.747 |   24.9 |   66.4 |    47.1
   5 |  0.641 |    0.201 |    0.229 |    0.576 |    0.840 |   40.3 |   73.7 |    61.7

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.440±0.103, Πᵢⱼ=0.732±0.101, PoC=0.854
PoC calculation for dose 3: Πᵢ=0.503±0.091, Πᵢⱼ=0.732±0.101, PoC=0.759
PoC calculation for dose 4: Πᵢ=0.508±0.101, Πᵢⱼ=0.732±0.101, PoC=0.724
PoC calculation for dose 5: Πᵢ=0.732±0.101, Πᵢⱼ=0.732±0.101, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0.854 
PoC threshold: 0.9 
PoC threshold met: FALSE 
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 3 4 5 
Utilities: 27.83 42.55 47.06 61.69 
Selected dose: 5 
Selected utility: 61.69 
PoC validated: FALSE 
Max PoC probability: 0.854 
Selection reason: PoC threshold not met, but selecting best available dose 
--- END FINAL SELECTION ---

Results

This chunk prints the final optimal dose and displays the plots.

# Print final results
cat("
--- Final Results ---
")

--- Final Results ---

if (results$terminated_early) {
  cat("Trial terminated early at stage:", results$termination_stage, "
")
  cat("Reason:", results$termination_reason, "
")
  cat("No Optimal Dose selected
")
} else {
  cat("Final OD:", results$final_od, "
")
  cat("Final utility:", round(results$final_utility, 2), "
")
  cat("PoC validated:", results$poc_validated, "
")
  cat("PoC probability:", round(results$poc_probability, 3), "
")
  cat("Selection reason:", results$selection_reason, "
")
}

Final OD: 5 
Final utility: 61.69 
PoC validated: FALSE 
PoC probability: 0.854 
Selection reason: PoC threshold not met, but selecting best available dose 

# Plot final results and save them with modern styling
plot_posterior_summary(results$posterior_summaries$imm, title = "Immune Response vs Dose (PAVA Adjusted)", file_path = "results/plots/immune_response_refactored.png", style = "modern")

plot_posterior_summary(results$posterior_summaries$tox, title = "Toxicity Rate by Dose and Immune Status", group_col = "Y_I", file_path = "results/plots/toxicity_refactored.png", style = "modern")

plot_posterior_summary(results$posterior_summaries$eff, title = "Efficacy Rate by Dose and Immune Status", group_col = "Y_I", file_path = "results/plots/efficacy_refactored.png", style = "modern")

# Create dose-response curves similar to reference code
cat("\n=== Creating Dose-Response Curves ===\n")

=== Creating Dose-Response Curves ===

# Extract true probabilities for dose-response curves
true_toxicity <- p_YT_given_I[,1] * (1 - p_YI) + p_YT_given_I[,2] * p_YI
true_efficacy <- p_YE_given_I[,1] * (1 - p_YI) + p_YE_given_I[,2] * p_YI
true_utility <- results$final_utility_by_dose

# Create dose-response curves plot
dose_response_plot <- plot_dose_response_curves(
  toxicity_data = true_toxicity,
  efficacy_data = true_efficacy,
  utility_data = true_utility,
  title = "True Dose-Response Curves",
  file_path = "results/plots/dose_response_curves.png"
)

Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_line()`).

Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_point()`).

print(dose_response_plot)

Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_line()`).
Removed 3 rows containing missing values or values outside the scale range
(`geom_point()`).

# Plot allocation probabilities over time with modern styling
p_alloc_time <- ggplot(results$all_alloc_probs, aes(x = Stage, y = Prob, color = factor(Dose))) +
  geom_line(linewidth = 1) +
  geom_point(size = 3) +
  labs(title = "Allocation Probabilities Over Time", 
       x = "Stage", y = "Allocation Probability", 
       color = "Dose Level") +
  scale_color_manual(values = c("#999999", "#E69F00", "#56B4E9", "#009E73", "#CC79A7")) +
  theme_bw(base_size = 16) +
  theme(panel.grid = element_blank(),
        plot.title = element_text(hjust = 0.5),
        axis.line = element_line(color = "black"))
print(p_alloc_time)

# Visualize participant allocation with better formatting
# Count participants per dose level and stage
allocation_summary <- results$all_data %>%
  group_by(d, stage) %>%
  summarise(n_participants = n(), .groups = 'drop') %>%
  mutate(d = factor(d), stage = factor(stage, levels = 1:5, labels = paste("Stage", 1:5)))

# Plot 1: Allocation by dose level and stage with modern styling
p_alloc <- ggplot(allocation_summary, aes(x = d, y = n_participants, fill = stage)) +
  geom_bar(stat = "identity", position = "dodge", width = 0.7, color = "black") +
  labs(title = "Participant Allocation by Dose Level and Stage", 
       x = "Dose Level", y = "Number of Participants",
       subtitle = paste("Total participants:", sum(allocation_summary$n_participants))) +
  scale_fill_manual(name = "Stage", values = c("#999999", "#E69F00", "#56B4E9", "#009E73", "#CC79A7")) +
  theme_bw(base_size = 16) +
  theme(panel.grid = element_blank(),
        plot.title = element_text(size = 14, face = "bold", hjust = 0.5),
        axis.text = element_text(size = 12),
        axis.title = element_text(size = 12),
        axis.line = element_line(color = "black"))
print(p_alloc)

# Plot 2: Cumulative allocation over stages
cumulative_summary <- allocation_summary %>%
  group_by(d) %>%
  mutate(cumulative_participants = cumsum(n_participants)) %>%
  ungroup()

p_cumulative <- ggplot(cumulative_summary, aes(x = stage, y = cumulative_participants, color = d, group = d)) +
  geom_line(linewidth = 1.5) +
  geom_point(size = 3) +
  labs(title = "Cumulative Participant Allocation Over Stages", 
       x = "Stage", y = "Cumulative Number of Participants",
       color = "Dose Level",
       subtitle = paste("Final total participants:", sum(allocation_summary$n_participants))) +
  scale_color_manual(values = c("#999999", "#E69F00", "#56B4E9", "#009E73", "#CC79A7")) +
  theme_bw(base_size = 16) +
  theme(panel.grid = element_blank(),
        plot.title = element_text(size = 14, face = "bold", hjust = 0.5),
        axis.text = element_text(size = 12),
        axis.title = element_text(size = 12),
        axis.line = element_line(color = "black"))
print(p_cumulative)

# Print summary statistics
cat("\n=== ALLOCATION SUMMARY ===\n")

=== ALLOCATION SUMMARY ===

cat("Total participants:", sum(allocation_summary$n_participants), "\n")

Total participants: 75 

cat("Participants per stage:\n")

Participants per stage:

stage_totals <- allocation_summary %>%
  group_by(stage) %>%
  summarise(total = sum(n_participants), .groups = 'drop')
for(i in 1:nrow(stage_totals)) {
  cat("  Stage", i, ":", stage_totals$total[i], "participants\n")
}

  Stage 1 : 15 participants
  Stage 2 : 15 participants
  Stage 3 : 15 participants
  Stage 4 : 15 participants
  Stage 5 : 15 participants

Method Comparison Analysis

This section creates comparison plots similar to the reference code, showing how different methods or parameter settings would perform.

# Create example data for method comparison (similar to reference code)
cat("\n=== Creating Method Comparison Plots ===\n")

=== Creating Method Comparison Plots ===

# Simulate different method performances
methods <- c("Current", "Proposed", "Reference")
scenarios <- c("Scenario 1", "Scenario 2", "Scenario 3")

# OBD Selection Rate Comparison
obd_data <- expand.grid(
  scenario = scenarios,
  method = methods,
  stringsAsFactors = FALSE
)
obd_data$obd_rate <- c(45, 60, 55, 70, 65, 50, 80, 85, 75)

# Create OBD selection plot
p_obd <- plot_method_comparison_bars(
  obd_data,
  x_var = "scenario", y_var = "obd_rate", fill_var = "method",
  title = "OBD Selection Rate Comparison",
  y_label = "OBD Selection (%)",
  limits = c(0, 100),
  file_path = "results/plots/obd_selection_comparison.png"
)

Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
ℹ Please use tidy evaluation idioms with `aes()`.
ℹ See also `vignette("ggplot2-in-packages")` for more information.

print(p_obd)

# Sample Size Comparison
sample_data <- expand.grid(
  scenario = scenarios,
  method = methods,
  stringsAsFactors = FALSE
)
sample_data$avg_n <- c(25, 20, 30, 22, 18, 28, 18, 15, 25)

# Create sample size plot
p_sample <- plot_method_comparison_bars(
  sample_data,
  x_var = "scenario", y_var = "avg_n", fill_var = "method",
  title = "Average Sample Size Comparison",
  y_label = "Average Sample Size",
  limits = c(0, 35),
  file_path = "results/plots/sample_size_comparison.png"
)
print(p_sample)

# Safety (Overdose) Comparison
safety_data <- expand.grid(
  scenario = scenarios,
  method = methods,
  stringsAsFactors = FALSE
)
safety_data$overdose_pct <- c(15, 10, 20, 12, 8, 18, 8, 5, 15)

# Create safety plot
p_safety <- plot_method_comparison_bars(
  safety_data,
  x_var = "scenario", y_var = "overdose_pct", fill_var = "method",
  title = "Overdose Patient Percentage",
  y_label = "Overdose Pts (%)",
  limits = c(0, 25),
  file_path = "results/plots/safety_comparison.png"
)
print(p_safety)

cat("✅ Method comparison plots created successfully!\n")

✅ Method comparison plots created successfully!

cat("📁 All plots saved to results/plots/ directory\n")

📁 All plots saved to results/plots/ directory

Multi-Scenario Analysis

This section creates multi-scenario dose-response curves similar to the reference code.

# Create multi-scenario analysis
cat("\n=== Creating Multi-Scenario Analysis ===\n")

=== Creating Multi-Scenario Analysis ===

# Define different scenarios with varying parameters
scenarios_data <- list(
  list(
    toxicity = c(0.1, 0.18, 0.35, 0.40, 0.50),
    efficacy = c(0.35, 0.35, 0.37, 0.39, 0.39),
    utility = c(0.27, 0.23, 0.10, 0.13, 0.17)
  ),
  list(
    toxicity = c(0.05, 0.15, 0.25, 0.35, 0.50),
    efficacy = c(0.10, 0.35, 0.35, 0.38, 0.39),
    utility = c(0.07, 0.22, 0.22, 0.12, 0.06)
  ),
  list(
    toxicity = c(0.02, 0.06, 0.10, 0.20, 0.35),
    efficacy = c(0.05, 0.10, 0.35, 0.35, 0.40),
    utility = c(0.03, 0.07, 0.28, 0.22, 0.13)
  )
)

# Create multi-scenario plot
multi_scenario_plot <- plot_multi_scenario_curves(
  scenarios_data,
  title = "Dose-Response Curves Across Scenarios",
  file_path = "results/plots/multi_scenario_analysis.png"
)

Scale for y is already present.
Adding another scale for y, which will replace the existing scale.

print(multi_scenario_plot)

cat("✅ Multi-scenario analysis completed!\n")

✅ Multi-scenario analysis completed!

Calibration Framework

This section demonstrates the calibration framework for optimizing trial parameters.

Setup Calibration

# Use absolute paths for calibration functions
project_root <- "/Users/jz/Development/DoseFinding"

# Source calibration functions
source(file.path(project_root, "src/optimization/poc_calibration.R"))
source(file.path(project_root, "src/optimization/early_termination_calibration.R"))
source(file.path(project_root, "src/utils/calibration_plots.R"))

# Set up output directory for calibration results
calibration_output_dir <- "results/notebook_calibration"
dir.create(calibration_output_dir, showWarnings = FALSE, recursive = TRUE)

PoC Calibration

Calibrate the PoC threshold to achieve target detection rates in null scenarios.

# Run PoC calibration with reduced simulations for notebook
cat("Running PoC calibration...\n")

Running PoC calibration...

poc_results <- run_quick_calibration(
  target_rate = 0.10,
  n_simulations = 100  # Reduced for notebook
)

Running quick calibration (reduced simulations for testing)...
Starting PoC calibration...
Target detection rate: 0.1 
Number of simulations per C_poc: 100 
C_poc range: 0.7 to 0.95 

Progress: 1/6 - Testing C_poc = 0.700

--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428 
Summary: Efficacy marginal means: 0.556 0.629 0.664 
Summary: Immune response means: 0.285 0.305 0.357 
Dose 1 : P(Tox <  0.3 ) =  0.73 (Threshold:  0.5 ) P(Eff >  0.2 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.76 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.45 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.8 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.18 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.87 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.285 
  Toxicity given I=0 (π_T|I=0): 0.194 
  Toxicity given I=1 (π_T|I=1): 0.335 
  Efficacy given I=0 (π_E|I=0): 0.531 
  Efficacy given I=1 (π_E|I=1): 0.62 
  Probability distributions:
    P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 
    P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 
    P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 
    P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 
  Expected utility given I=0: 37.35 
  Expected utility given I=1: 52.03 
  Total expected utility: 41.54 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.305 
  Toxicity given I=0 (π_T|I=0): 0.247 
  Toxicity given I=1 (π_T|I=1): 0.496 
  Efficacy given I=0 (π_E|I=0): 0.615 
  Efficacy given I=1 (π_E|I=1): 0.662 
  Probability distributions:
    P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 
    P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 
    P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 
    P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 
  Expected utility given I=0: 41.58 
  Expected utility given I=1: 48.22 
  Total expected utility: 43.61 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.357 
  Toxicity given I=0 (π_T|I=0): 0.32 
  Toxicity given I=1 (π_T|I=1): 0.626 
  Efficacy given I=0 (π_E|I=0): 0.634 
  Efficacy given I=1 (π_E|I=1): 0.717 
  Probability distributions:
    P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 
    P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 
    P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 
    P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 
  Expected utility given I=0: 40.58 
  Expected utility given I=1: 45.83 
  Total expected utility: 42.46 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.285 |    0.194 |    0.335 |    0.531 |    0.620 |   37.4 |   52.0 |    41.5
   2 |  0.305 |    0.247 |    0.496 |    0.615 |    0.662 |   41.6 |   48.2 |    43.6
   3 |  0.357 |    0.320 |    0.626 |    0.634 |    0.717 |   40.6 |   45.8 |    42.5

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0 

--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416 
Summary: Efficacy marginal means: 0.644 0.675 0.699 
Summary: Immune response means: 0.237 0.276 0.344 
Dose 1 : P(Tox <  0.3 ) =  0.95 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.63 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.57 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.73 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.22 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.86 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 1 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.237 
  Toxicity given I=0 (π_T|I=0): 0.109 
  Toxicity given I=1 (π_T|I=1): 0.255 
  Efficacy given I=0 (π_E|I=0): 0.632 
  Efficacy given I=1 (π_E|I=1): 0.688 
  Probability distributions:
    P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 
    P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 
    P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 
    P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 
  Expected utility given I=0: 47.08 
  Expected utility given I=1: 60.58 
  Total expected utility: 50.27 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.276 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.483 
  Efficacy given I=0 (π_E|I=0): 0.663 
  Efficacy given I=1 (π_E|I=1): 0.706 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 
    P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 
    P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 
  Expected utility given I=0: 45.79 
  Expected utility given I=1: 51.67 
  Total expected utility: 47.42 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.344 
  Toxicity given I=0 (π_T|I=0): 0.309 
  Toxicity given I=1 (π_T|I=1): 0.62 
  Efficacy given I=0 (π_E|I=0): 0.676 
  Efficacy given I=1 (π_E|I=1): 0.744 
  Probability distributions:
    P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 
    P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 
    P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 
    P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 
  Expected utility given I=0: 43.64 
  Expected utility given I=1: 47.71 
  Total expected utility: 45.04 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.237 |    0.109 |    0.255 |    0.632 |    0.688 |   47.1 |   60.6 |    50.3
   2 |  0.276 |    0.218 |    0.483 |    0.663 |    0.706 |   45.8 |   51.7 |    47.4
   3 |  0.344 |    0.309 |    0.620 |    0.676 |    0.744 |   43.6 |   47.7 |    45.0

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0 

--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391 
Summary: Efficacy marginal means: 0.694 0.709 0.725 
Summary: Immune response means: 0.204 0.219 0.316 
Dose 1 : P(Tox <  0.3 ) =  0.99 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.48 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.3 ) =  0.8 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.3 ) =  0.29 (Threshold:  0.5 ) P(Eff >  0.2 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.77 (Threshold:  0.5 )
>>>>>>> origin/main
--- End Admissibility Check ---
Admissible set: 2 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
<<<<<<< HEAD
  Immune response probability (π_I): 0.158 
  Toxicity given I=0 (π_T|I=0): 0.233 
  Toxicity given I=1 (π_T|I=1): 0.356 
  Efficacy given I=0 (π_E|I=0): 0.141 
  Efficacy given I=1 (π_E|I=1): 0.332 
  Probability distributions:
    P(T=0|I=0): 0.767 P(T=1|I=0): 0.233 
    P(T=0|I=1): 0.644 P(T=1|I=1): 0.356 
    P(E=0|I=0): 0.859 P(E=1|I=0): 0.141 
    P(E=0|I=1): 0.668 P(E=1|I=1): 0.332 
  Expected utility given I=0: 9.61 
  Expected utility given I=1: 30.43 
  Total expected utility: 12.89 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.239 
  Toxicity given I=0 (π_T|I=0): 0.252 
  Toxicity given I=1 (π_T|I=1): 0.393 
  Efficacy given I=0 (π_E|I=0): 0.214 
  Efficacy given I=1 (π_E|I=1): 0.387 
  Probability distributions:
    P(T=0|I=0): 0.748 P(T=1|I=0): 0.252 
    P(T=0|I=1): 0.607 P(T=1|I=1): 0.393 
    P(E=0|I=0): 0.786 P(E=1|I=0): 0.214 
    P(E=0|I=1): 0.613 P(E=1|I=1): 0.387 
  Expected utility given I=0: 14.41 
  Expected utility given I=1: 33.29 
  Total expected utility: 18.93 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.531 
  Toxicity given I=0 (π_T|I=0): 0.326 
  Toxicity given I=1 (π_T|I=1): 0.411 
  Efficacy given I=0 (π_E|I=0): 0.302 
  Efficacy given I=1 (π_E|I=1): 0.405 
  Probability distributions:
    P(T=0|I=0): 0.674 P(T=1|I=0): 0.326 
    P(T=0|I=1): 0.589 P(T=1|I=1): 0.411 
    P(E=0|I=0): 0.698 P(E=1|I=0): 0.302 
    P(E=0|I=1): 0.595 P(E=1|I=1): 0.405 
  Expected utility given I=0: 19.25 
  Expected utility given I=1: 34.05 
  Total expected utility: 27.11 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.604 
  Toxicity given I=0 (π_T|I=0): 0.52 
  Toxicity given I=1 (π_T|I=1): 0.571 
  Efficacy given I=0 (π_E|I=0): 0.46 
  Efficacy given I=1 (π_E|I=1): 0.562 
  Probability distributions:
    P(T=0|I=0): 0.48 P(T=1|I=0): 0.52 
    P(T=0|I=1): 0.429 P(T=1|I=1): 0.571 
    P(E=0|I=0): 0.54 P(E=1|I=0): 0.46 
    P(E=0|I=1): 0.438 P(E=1|I=1): 0.562 
  Expected utility given I=0: 24.83 
  Expected utility given I=1: 38.8 
  Total expected utility: 33.28 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.684 
  Toxicity given I=0 (π_T|I=0): 0.611 
  Toxicity given I=1 (π_T|I=1): 0.659 
  Efficacy given I=0 (π_E|I=0): 0.492 
  Efficacy given I=1 (π_E|I=1): 0.778 
  Probability distributions:
    P(T=0|I=0): 0.389 P(T=1|I=0): 0.611 
    P(T=0|I=1): 0.341 P(T=1|I=1): 0.659 
    P(E=0|I=0): 0.508 P(E=1|I=0): 0.492 
    P(E=0|I=1): 0.222 P(E=1|I=1): 0.778 
  Expected utility given I=0: 24.33 
  Expected utility given I=1: 47.78 
  Total expected utility: 40.37 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.158 |    0.233 |    0.356 |    0.141 |    0.332 |    9.6 |   30.4 |    12.9
   2 |  0.239 |    0.252 |    0.393 |    0.214 |    0.387 |   14.4 |   33.3 |    18.9
   3 |  0.531 |    0.326 |    0.411 |    0.302 |    0.405 |   19.3 |   34.1 |    27.1
   4 |  0.604 |    0.520 |    0.571 |    0.460 |    0.562 |   24.8 |   38.8 |    33.3
   5 |  0.684 |    0.611 |    0.659 |    0.492 |    0.778 |   24.3 |   47.8 |    40.4

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 1 0 0 0 

--- Stage 2 ---
Workflow: Step 1 - Adaptive randomization (using probabilities from previous stage)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.104 0.12 0.302 0.543 0.639 
Summary: Efficacy marginal means: 0.121 0.158 0.3 0.516 0.68 
Summary: Immune response means: 0.144 0.216 0.526 0.6 0.68 
Dose 1 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.59 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.27 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.82 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.53 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  0.67 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.98 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  0.07 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.01 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.144 
  Toxicity given I=0 (π_T|I=0): 0.082 
  Toxicity given I=1 (π_T|I=1): 0.233 
  Efficacy given I=0 (π_E|I=0): 0.102 
  Efficacy given I=1 (π_E|I=1): 0.233 
  Probability distributions:
    P(T=0|I=0): 0.918 P(T=1|I=0): 0.082 
    P(T=0|I=1): 0.767 P(T=1|I=1): 0.233 
    P(E=0|I=0): 0.898 P(E=1|I=0): 0.102 
    P(E=0|I=1): 0.767 P(E=1|I=1): 0.233 
  Expected utility given I=0: 7.71 
  Expected utility given I=1: 25.93 
  Total expected utility: 10.33 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.216 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.256 
  Efficacy given I=0 (π_E|I=0): 0.132 
  Efficacy given I=1 (π_E|I=1): 0.255 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.744 P(T=1|I=1): 0.256 
    P(E=0|I=0): 0.868 P(E=1|I=0): 0.132 
    P(E=0|I=1): 0.745 P(E=1|I=1): 0.255 
  Expected utility given I=0: 9.99 
  Expected utility given I=1: 27.15 
  Total expected utility: 13.7 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.526 
  Toxicity given I=0 (π_T|I=0): 0.251 
  Toxicity given I=1 (π_T|I=1): 0.348 
  Efficacy given I=0 (π_E|I=0): 0.257 
  Efficacy given I=1 (π_E|I=1): 0.34 
  Probability distributions:
    P(T=0|I=0): 0.749 P(T=1|I=0): 0.251 
    P(T=0|I=1): 0.652 P(T=1|I=1): 0.348 
    P(E=0|I=0): 0.743 P(E=1|I=0): 0.257 
    P(E=0|I=1): 0.66 P(E=1|I=1): 0.34 
  Expected utility given I=0: 17.32 
  Expected utility given I=1: 31.2 
  Total expected utility: 24.62 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.6 
  Toxicity given I=0 (π_T|I=0): 0.509 
  Toxicity given I=1 (π_T|I=1): 0.566 
  Efficacy given I=0 (π_E|I=0): 0.451 
  Efficacy given I=1 (π_E|I=1): 0.557 
  Probability distributions:
    P(T=0|I=0): 0.491 P(T=1|I=0): 0.509 
    P(T=0|I=1): 0.434 P(T=1|I=1): 0.566 
    P(E=0|I=0): 0.549 P(E=1|I=0): 0.451 
    P(E=0|I=1): 0.443 P(E=1|I=1): 0.557 
  Expected utility given I=0: 24.6 
  Expected utility given I=1: 38.74 
  Total expected utility: 33.09 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.68 
  Toxicity given I=0 (π_T|I=0): 0.607 
  Toxicity given I=1 (π_T|I=1): 0.654 
  Efficacy given I=0 (π_E|I=0): 0.491 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.393 P(T=1|I=0): 0.607 
    P(T=0|I=1): 0.346 P(T=1|I=1): 0.654 
    P(E=0|I=0): 0.509 P(E=1|I=0): 0.491 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 24.38 
  Expected utility given I=1: 47.46 
  Total expected utility: 40.07 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.144 |    0.082 |    0.233 |    0.102 |    0.233 |    7.7 |   25.9 |    10.3
   2 |  0.216 |    0.083 |    0.256 |    0.132 |    0.255 |   10.0 |   27.2 |    13.7
   3 |  0.526 |    0.251 |    0.348 |    0.257 |    0.340 |   17.3 |   31.2 |    24.6
   4 |  0.600 |    0.509 |    0.566 |    0.451 |    0.557 |   24.6 |   38.7 |    33.1
   5 |  0.680 |    0.607 |    0.654 |    0.491 |    0.768 |   24.4 |   47.5 |    40.1

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.3575546 0.6424454 0 0 

--- Stage 3 ---
Workflow: Step 1 - Adaptive randomization (using probabilities from previous stage)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.082 0.097 0.242 0.531 0.638 
Summary: Efficacy marginal means: 0.153 0.212 0.441 0.544 0.697 
Summary: Immune response means: 0.17 0.295 0.557 0.618 0.683 
Dose 1 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.74 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.4 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.97 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.88 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  0.88 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  0.08 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.01 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.17 
  Toxicity given I=0 (π_T|I=0): 0.067 
  Toxicity given I=1 (π_T|I=1): 0.155 
  Efficacy given I=0 (π_E|I=0): 0.127 
  Efficacy given I=1 (π_E|I=1): 0.277 
  Probability distributions:
    P(T=0|I=0): 0.933 P(T=1|I=0): 0.067 
    P(T=0|I=1): 0.845 P(T=1|I=1): 0.155 
    P(E=0|I=0): 0.873 P(E=1|I=0): 0.127 
    P(E=0|I=1): 0.723 P(E=1|I=1): 0.277 
  Expected utility given I=0: 9.71 
  Expected utility given I=1: 31.24 
  Total expected utility: 13.38 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.295 
  Toxicity given I=0 (π_T|I=0): 0.068 
  Toxicity given I=1 (π_T|I=1): 0.165 
  Efficacy given I=0 (π_E|I=0): 0.171 
  Efficacy given I=1 (π_E|I=1): 0.311 
  Probability distributions:
    P(T=0|I=0): 0.932 P(T=1|I=0): 0.068 
    P(T=0|I=1): 0.835 P(T=1|I=1): 0.165 
    P(E=0|I=0): 0.829 P(E=1|I=0): 0.171 
    P(E=0|I=1): 0.689 P(E=1|I=1): 0.311 
  Expected utility given I=0: 13.07 
  Expected utility given I=1: 33.79 
  Total expected utility: 19.18 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.557 
  Toxicity given I=0 (π_T|I=0): 0.218 
  Toxicity given I=1 (π_T|I=1): 0.259 
  Efficacy given I=0 (π_E|I=0): 0.374 
  Efficacy given I=1 (π_E|I=1): 0.494 
  Probability distributions:
    P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 
    P(T=0|I=1): 0.741 P(T=1|I=1): 0.259 
    P(E=0|I=0): 0.626 P(E=1|I=0): 0.374 
    P(E=0|I=1): 0.506 P(E=1|I=1): 0.494 
  Expected utility given I=0: 25.82 
  Expected utility given I=1: 45.46 
  Total expected utility: 36.77 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.618 
  Toxicity given I=0 (π_T|I=0): 0.5 
  Toxicity given I=1 (π_T|I=1): 0.55 
  Efficacy given I=0 (π_E|I=0): 0.481 
  Efficacy given I=1 (π_E|I=1): 0.583 
  Probability distributions:
    P(T=0|I=0): 0.5 P(T=1|I=0): 0.5 
    P(T=0|I=1): 0.45 P(T=1|I=1): 0.55 
    P(E=0|I=0): 0.519 P(E=1|I=0): 0.481 
    P(E=0|I=1): 0.417 P(E=1|I=1): 0.583 
  Expected utility given I=0: 26.45 
  Expected utility given I=1: 40.96 
  Total expected utility: 35.42 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.683 
  Toxicity given I=0 (π_T|I=0): 0.606 
  Toxicity given I=1 (π_T|I=1): 0.653 
  Efficacy given I=0 (π_E|I=0): 0.513 
  Efficacy given I=1 (π_E|I=1): 0.782 
  Probability distributions:
    P(T=0|I=0): 0.394 P(T=1|I=0): 0.606 
    P(T=0|I=1): 0.347 P(T=1|I=1): 0.653 
    P(E=0|I=0): 0.487 P(E=1|I=0): 0.513 
    P(E=0|I=1): 0.218 P(E=1|I=1): 0.782 
  Expected utility given I=0: 25.49 
  Expected utility given I=1: 48.32 
  Total expected utility: 41.08 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.170 |    0.067 |    0.155 |    0.127 |    0.277 |    9.7 |   31.2 |    13.4
   2 |  0.295 |    0.068 |    0.165 |    0.171 |    0.311 |   13.1 |   33.8 |    19.2
   3 |  0.557 |    0.218 |    0.259 |    0.374 |    0.494 |   25.8 |   45.5 |    36.8
   4 |  0.618 |    0.500 |    0.550 |    0.481 |    0.583 |   26.5 |   41.0 |    35.4
   5 |  0.683 |    0.606 |    0.653 |    0.513 |    0.782 |   25.5 |   48.3 |    41.1

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.3428895 0.6571105 0 0 

--- Stage 4 ---
Workflow: Step 1 - Adaptive randomization (using probabilities from previous stage)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.071 0.083 0.191 0.524 0.632 
Summary: Efficacy marginal means: 0.156 0.239 0.488 0.579 0.709 
Summary: Immune response means: 0.173 0.306 0.58 0.628 0.694 
Dose 1 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.74 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.39 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.99 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.9 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  0.98 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  0.11 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.02 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.173 
  Toxicity given I=0 (π_T|I=0): 0.06 
  Toxicity given I=1 (π_T|I=1): 0.125 
  Efficacy given I=0 (π_E|I=0): 0.113 
  Efficacy given I=1 (π_E|I=1): 0.357 
  Probability distributions:
    P(T=0|I=0): 0.94 P(T=1|I=0): 0.06 
    P(T=0|I=1): 0.875 P(T=1|I=1): 0.125 
    P(E=0|I=0): 0.887 P(E=1|I=0): 0.113 
    P(E=0|I=1): 0.643 P(E=1|I=1): 0.357 
  Expected utility given I=0: 8.73 
  Expected utility given I=1: 38.67 
  Total expected utility: 13.9 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.306 
  Toxicity given I=0 (π_T|I=0): 0.061 
  Toxicity given I=1 (π_T|I=1): 0.132 
  Efficacy given I=0 (π_E|I=0): 0.155 
  Efficacy given I=1 (π_E|I=1): 0.43 
  Probability distributions:
    P(T=0|I=0): 0.939 P(T=1|I=0): 0.061 
    P(T=0|I=1): 0.868 P(T=1|I=1): 0.132 
    P(E=0|I=0): 0.845 P(E=1|I=0): 0.155 
    P(E=0|I=1): 0.57 P(E=1|I=1): 0.43 
  Expected utility given I=0: 11.89 
  Expected utility given I=1: 44.49 
  Total expected utility: 21.88 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.58 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.22 
  Efficacy given I=0 (π_E|I=0): 0.346 
  Efficacy given I=1 (π_E|I=1): 0.593 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.78 P(T=1|I=1): 0.22 
    P(E=0|I=0): 0.654 P(E=1|I=0): 0.346 
    P(E=0|I=1): 0.407 P(E=1|I=1): 0.593 
  Expected utility given I=0: 25.05 
  Expected utility given I=1: 54.65 
  Total expected utility: 42.2 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.628 
  Toxicity given I=0 (π_T|I=0): 0.49 
  Toxicity given I=1 (π_T|I=1): 0.544 
  Efficacy given I=0 (π_E|I=0): 0.488 
  Efficacy given I=1 (π_E|I=1): 0.634 
  Probability distributions:
    P(T=0|I=0): 0.51 P(T=1|I=0): 0.49 
    P(T=0|I=1): 0.456 P(T=1|I=1): 0.544 
    P(E=0|I=0): 0.512 P(E=1|I=0): 0.488 
    P(E=0|I=1): 0.366 P(E=1|I=1): 0.634 
  Expected utility given I=0: 27.08 
  Expected utility given I=1: 44.37 
  Total expected utility: 37.95 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.694 
  Toxicity given I=0 (π_T|I=0): 0.598 
  Toxicity given I=1 (π_T|I=1): 0.646 
  Efficacy given I=0 (π_E|I=0): 0.521 
  Efficacy given I=1 (π_E|I=1): 0.793 
  Probability distributions:
    P(T=0|I=0): 0.402 P(T=1|I=0): 0.598 
    P(T=0|I=1): 0.354 P(T=1|I=1): 0.646 
    P(E=0|I=0): 0.479 P(E=1|I=0): 0.521 
    P(E=0|I=1): 0.207 P(E=1|I=1): 0.793 
  Expected utility given I=0: 26.08 
  Expected utility given I=1: 49.26 
  Total expected utility: 42.17 

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
   1 |  0.173 |    0.060 |    0.125 |    0.113 |    0.357 |    8.7 |   38.7 |    13.9
   2 |  0.306 |    0.061 |    0.132 |    0.155 |    0.430 |   11.9 |   44.5 |    21.9
   3 |  0.580 |    0.151 |    0.220 |    0.346 |    0.593 |   25.1 |   54.6 |    42.2
   4 |  0.628 |    0.490 |    0.544 |    0.488 |    0.634 |   27.1 |   44.4 |    37.9
   5 |  0.694 |    0.598 |    0.646 |    0.521 |    0.793 |   26.1 |   49.3 |    42.2

--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.3414691 0.6585309 0 0 

--- Stage 5 ---
Workflow: Step 1 - Adaptive randomization (using probabilities from previous stage)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)

--- Admissibility Check ---
Summary: Toxicity marginal means: 0.061 0.072 0.22 0.536 0.635 
Summary: Efficacy marginal means: 0.152 0.254 0.498 0.593 0.712 
Summary: Immune response means: 0.168 0.321 0.581 0.635 0.699 
Dose 1 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  0.74 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.38 (Threshold:  0.5 )
Dose 2 : P(Tox <  0.35 ) =  1 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  0.95 (Threshold:  0.5 )
Dose 3 : P(Tox <  0.35 ) =  0.97 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 4 : P(Tox <  0.35 ) =  0.09 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
Dose 5 : P(Tox <  0.35 ) =  0.01 (Threshold:  0.5 ) P(Eff >  0.1 ) =  1 (Threshold:  0.5 ) P(Imm >  0.2 ) =  1 (Threshold:  0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 
Workflow: Step 4 - Early Termination Check

--- Utility Score Calculations ---
Utility Table Reference:
  I=0 (No Immune Response):
    E=0, T=0: 0   E=1, T=0: 80 
    E=0, T=1: 0   E=1, T=1: 30 
  I=1 (Immune Response):
    E=0, T=0: 10   E=1, T=0: 100 
    E=0, T=1: 0   E=1, T=1: 40 

Dose 1 Utility Calculation:
  Immune response probability (π_I): 0.168 
  Toxicity given I=0 (π_T|I=0): 0.05 
  Toxicity given I=1 (π_T|I=1): 0.113 
  Efficacy given I=0 (π_E|I=0): 0.104 
  Efficacy given I=1 (π_E|I=1): 0.396 
  Probability distributions:
    P(T=0|I=0): 0.95 P(T=1|I=0): 0.05 
    P(T=0|I=1): 0.887 P(T=1|I=1): 0.113 
    P(E=0|I=0): 0.896 P(E=1|I=0): 0.104 
    P(E=0|I=1): 0.604 P(E=1|I=1): 0.396 
  Expected utility given I=0: 8.03 
  Expected utility given I=1: 42.29 
  Total expected utility: 13.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.321 
  Toxicity given I=0 (π_T|I=0): 0.051 
  Toxicity given I=1 (π_T|I=1): 0.118 
  Efficacy given I=0 (π_E|I=0): 0.134 
  Efficacy given I=1 (π_E|I=1): 0.508 
  Probability distributions:
    P(T=0|I=0): 0.949 P(T=1|I=0): 0.051 
    P(T=0|I=1): 0.882 P(T=1|I=1): 0.118 
    P(E=0|I=0): 0.866 P(E=1|I=0): 0.134 
    P(E=0|I=1): 0.492 P(E=1|I=1): 0.508 
  Expected utility given I=0: 10.38 
  Expected utility given I=1: 51.52 
  Total expected utility: 23.6 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.581 
  Toxicity given I=0 (π_T|I=0): 0.181 
  Toxicity given I=1 (π_T|I=1): 0.248 
  Efficacy given I=0 (π_E|I=0): 0.332 
  Efficacy given I=1 (π_E|I=1): 0.617 
  Probability distributions:
    P(T=0|I=0): 0.819 P(T=1|I=0): 0.181 
    P(T=0|I=1): 0.752 P(T=1|I=1): 0.248 
    P(E=0|I=0): 0.668 P(E=1|I=0): 0.332 
    P(E=0|I=1): 0.383 P(E=1|I=1): 0.617 
  Expected utility given I=0: 23.55 
  Expected utility given I=1: 55.43 
  Total expected utility: 42.06 

Dose 4 Utility Calculation:
  Immune response probability (π_I): 0.635 
  Toxicity given I=0 (π_T|I=0): 0.5 
  Toxicity given I=1 (π_T|I=1): 0.555 
  Efficacy given I=0 (π_E|I=0): 0.485 
  Efficacy given I=1 (π_E|I=1): 0.654 
  Probability distributions:
    P(T=0|I=0): 0.5 P(T=1|I=0): 0.5 
    P(T=0|I=1): 0.445 P(T=1|I=1): 0.555 
    P(E=0|I=0): 0.515 P(E=1|I=0): 0.485 
    P(E=0|I=1): 0.346 P(E=1|I=1): 0.654 
  Expected utility given I=0: 26.69 
  Expected utility given I=1: 45.15 
  Total expected utility: 38.4 

Dose 5 Utility Calculation:
  Immune response probability (π_I): 0.699 
  Toxicity given I=0 (π_T|I=0): 0.601 
  Toxicity given I=1 (π_T|I=1): 0.65 
  Efficacy given I=0 (π_E|I=0): 0.518 
  Efficacy given I=1 (π_E|I=1): 0.795 
  Probability distributions:
    P(T=0|I=0): 0.399 P(T=1|I=0): 0.601 
    P(T=0|I=1): 0.35 P(T=1|I=1): 0.65 
    P(E=0|I=0): 0.482 P(E=1|I=0): 0.518 
    P(E=0|I=1): 0.205 P(E=1|I=1): 0.795 
  Expected utility given I=0: 25.89 
  Expected utility given I=1: 49.21 
  Total expected utility: 42.2 
=======
  Immune response probability (π_I): 0.204 
  Toxicity given I=0 (π_T|I=0): 0.083 
  Toxicity given I=1 (π_T|I=1): 0.207 
  Efficacy given I=0 (π_E|I=0): 0.684 
  Efficacy given I=1 (π_E|I=1): 0.733 
  Probability distributions:
    P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 
    P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 
    P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 
    P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 
  Expected utility given I=0: 51.84 
  Expected utility given I=1: 66.29 
  Total expected utility: 54.79 

Dose 2 Utility Calculation:
  Immune response probability (π_I): 0.219 
  Toxicity given I=0 (π_T|I=0): 0.151 
  Toxicity given I=1 (π_T|I=1): 0.469 
  Efficacy given I=0 (π_E|I=0): 0.699 
  Efficacy given I=1 (π_E|I=1): 0.741 
  Probability distributions:
    P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 
    P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 
    P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 
    P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 
  Expected utility given I=0: 50.63 
  Expected utility given I=1: 54.65 
  Total expected utility: 51.51 

Dose 3 Utility Calculation:
  Immune response probability (π_I): 0.316 
  Toxicity given I=0 (π_T|I=0): 0.287 
  Toxicity given I=1 (π_T|I=1): 0.609 
  Efficacy given I=0 (π_E|I=0): 0.706 
  Efficacy given I=1 (π_E|I=1): 0.768 
  Probability distributions:
    P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 
    P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 
    P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 
    P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 
  Expected utility given I=0: 46.36 
  Expected utility given I=1: 49.63 
  Total expected utility: 47.4 
>>>>>>> origin/main

Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
<<<<<<< HEAD
   1 |  0.168 |    0.050 |    0.113 |    0.104 |    0.396 |    8.0 |   42.3 |    13.8
   2 |  0.321 |    0.051 |    0.118 |    0.134 |    0.508 |   10.4 |   51.5 |    23.6
   3 |  0.581 |    0.181 |    0.248 |    0.332 |    0.617 |   23.6 |   55.4 |    42.1
   4 |  0.635 |    0.500 |    0.555 |    0.485 |    0.654 |   26.7 |   45.1 |    38.4
   5 |  0.699 |    0.601 |    0.650 |    0.518 |    0.795 |   25.9 |   49.2 |    42.2

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation

--- PoC THRESHOLD CHECK ---
Admissible doses: 2 3 
Pairwise probabilities Pr(π_I1 < delta_poc * π_Ij | D_n): 0.703 0.986 
c_poc threshold: 0.95 
P_final (doses passing PoC): 3 
PoC detected (length(P_final) > 0): TRUE 
=======
   1 |  0.204 |    0.083 |    0.207 |    0.684 |    0.733 |   51.8 |   66.3 |    54.8
   2 |  0.219 |    0.151 |    0.469 |    0.699 |    0.741 |   50.6 |   54.7 |    51.5
   3 |  0.316 |    0.287 |    0.609 |    0.706 |    0.768 |   46.4 |   49.6 |    47.4

--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000

--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0 
PoC threshold: 0.7 
PoC threshold met: FALSE 
>>>>>>> origin/main
--- END PoC CHECK ---


--- FINAL DOSE SELECTION WITH PoC ---
<<<<<<< HEAD
Admissible doses A: 2 3 
Utilities: 23.6 42.06 
Pairwise probabilities Pr(π_I1 < delta*π_Ij): 0.703 0.986 
c_poc threshold: 0.95 
P_final (PoC-eligible doses): 3 
PoC detected: TRUE 
Selected dose: 3 
Selected utility: 42.06 
Selection reason: PoC detected (P_final non-empty) 
--- END FINAL SELECTION ---

Results

This chunk prints the final optimal dose and displays the plots.

# Print final results
cat("
--- Final Results ---
")

--- Final Results ---

if (results$terminated_early) {
  cat("Trial terminated early at stage:", results$termination_stage, "
")
  cat("Reason:", results$termination_reason, "
")
  cat("No Optimal Dose selected
")
} else {
  cat("Final OD:", results$final_od, "
")
  cat("Final utility:", round(results$final_utility, 2), "
")
  cat("PoC validated:", results$poc_validated, "
")
  cat("PoC probability:", round(results$poc_probability, 3), "
")
  cat("Selection reason:", results$selection_reason, "
")
}

Final OD: 3 
Final utility: 42.06 
PoC validated: TRUE 
PoC probability: 0.703 
Selection reason: PoC detected (P_final non-empty) 

# Plot final results and save them with modern styling
plot_posterior_summary(results$posterior_summaries$imm, title = "Immune Response vs Dose (PAVA Adjusted)", file_path = "results/plots/immune_response_refactored.png", style = "modern")

plot_posterior_summary(results$posterior_summaries$tox, title = "Toxicity Rate by Dose and Immune Status", group_col = "Y_I", file_path = "results/plots/toxicity_refactored.png", style = "modern")

plot_posterior_summary(results$posterior_summaries$eff, title = "Efficacy Rate by Dose and Immune Status", group_col = "Y_I", file_path = "results/plots/efficacy_refactored.png", style = "modern")

# Create dose-response curves similar to reference code
cat("\n=== Creating Dose-Response Curves ===\n")

=== Creating Dose-Response Curves ===

# Extract true probabilities for dose-response curves
true_toxicity <- p_YT_given_I[,1] * (1 - p_YI) + p_YT_given_I[,2] * p_YI
true_efficacy <- p_YE_given_I[,1] * (1 - p_YI) + p_YE_given_I[,2] * p_YI

# Calculate true utilities for all dose levels using true probabilities
true_utility <- sapply(1:length(trial_config$dose_levels), 
                       calculate_utility_from_true_probs, 
                       p_YI = p_YI, 
                       p_YT_given_I = p_YT_given_I, 
                       p_YE_given_I = p_YE_given_I,
                       utility_table = utility_table)

# Create dose-response curves plot
dose_response_plot <- plot_dose_response_curves(
  toxicity_data = true_toxicity,
  efficacy_data = true_efficacy,
  utility_data = true_utility,
  title = "True Dose-Response Curves",
  file_path = "results/plots/dose_response_curves.png"
)
print(dose_response_plot)

# Plot allocation probabilities over time with modern styling
p_alloc_time <- ggplot(results$all_alloc_probs, aes(x = Stage, y = Prob, color = factor(Dose))) +
  geom_line(linewidth = 1) +
  geom_point(size = 3) +
  labs(title = "Allocation Probabilities Over Time", 
       x = "Stage", y = "Allocation Probability", 
       color = "Dose Level") +
  scale_color_manual(values = c("#999999", "#E69F00", "#56B4E9", "#009E73", "#CC79A7")) +
  theme_bw(base_size = 16) +
  theme(panel.grid = element_blank(),
        plot.title = element_text(hjust = 0.5),
        axis.line = element_line(color = "black"))
print(p_alloc_time)

# Visualize participant allocation with better formatting
# Count participants per dose level and stage
allocation_summary <- results$all_data %>%
  group_by(d, stage) %>%
  summarise(n_participants = n(), .groups = 'drop') %>%
  mutate(d = factor(d), stage = factor(stage, levels = 1:5, labels = paste("Stage", 1:5)))

# Plot 1: Allocation by dose level and stage with modern styling
p_alloc <- ggplot(allocation_summary, aes(x = d, y = n_participants, fill = stage)) +
  geom_bar(stat = "identity", position = "dodge", width = 0.7, color = "black") +
  labs(title = "Participant Allocation by Dose Level and Stage", 
       x = "Dose Level", y = "Number of Participants",
       subtitle = paste("Total participants:", sum(allocation_summary$n_participants))) +
  scale_fill_manual(name = "Stage", values = c("#999999", "#E69F00", "#56B4E9", "#009E73", "#CC79A7")) +
  theme_bw(base_size = 16) +
  theme(panel.grid = element_blank(),
        plot.title = element_text(size = 14, face = "bold", hjust = 0.5),
        axis.text = element_text(size = 12),
        axis.title = element_text(size = 12),
        axis.line = element_line(color = "black"))
print(p_alloc)

# Plot 2: Cumulative allocation over stages
cumulative_summary <- allocation_summary %>%
  group_by(d) %>%
  mutate(cumulative_participants = cumsum(n_participants)) %>%
  ungroup()

p_cumulative <- ggplot(cumulative_summary, aes(x = stage, y = cumulative_participants, color = d, group = d)) +
  geom_line(linewidth = 1.5) +
  geom_point(size = 3) +
  labs(title = "Cumulative Participant Allocation Over Stages", 
       x = "Stage", y = "Cumulative Number of Participants",
       color = "Dose Level",
       subtitle = paste("Final total participants:", sum(allocation_summary$n_participants))) +
  scale_color_manual(values = c("#999999", "#E69F00", "#56B4E9", "#009E73", "#CC79A7")) +
  theme_bw(base_size = 16) +
  theme(panel.grid = element_blank(),
        plot.title = element_text(size = 14, face = "bold", hjust = 0.5),
        axis.text = element_text(size = 12),
        axis.title = element_text(size = 12),
        axis.line = element_line(color = "black"))
print(p_cumulative)

# Print summary statistics
cat("\n=== ALLOCATION SUMMARY ===\n")

=== ALLOCATION SUMMARY ===

cat("Total participants:", sum(allocation_summary$n_participants), "\n")

Total participants: 75 

cat("Participants per stage:\n")

Participants per stage:

stage_totals <- allocation_summary %>%
  group_by(stage) %>%
  summarise(total = sum(n_participants), .groups = 'drop')
for(i in 1:nrow(stage_totals)) {
  cat("  Stage", i, ":", stage_totals$total[i], "participants\n")
}

  Stage 1 : 15 participants
  Stage 2 : 15 participants
  Stage 3 : 15 participants
  Stage 4 : 15 participants
  Stage 5 : 15 participants

Method Comparison Analysis

This section creates comparison plots similar to the reference code, showing how different methods or parameter settings would perform.

# Create example data for method comparison (similar to reference code)
cat("\n=== Creating Method Comparison Plots ===\n")

=== Creating Method Comparison Plots ===

# Simulate different method performances
methods <- c("Current", "Proposed", "Reference")
scenarios <- c("Scenario 1", "Scenario 2", "Scenario 3")

# OBD Selection Rate Comparison
obd_data <- expand.grid(
  scenario = scenarios,
  method = methods,
  stringsAsFactors = FALSE
)
obd_data$obd_rate <- c(45, 60, 55, 70, 65, 50, 80, 85, 75)

# Create OBD selection plot
p_obd <- plot_method_comparison_bars(
  obd_data,
  x_var = "scenario", y_var = "obd_rate", fill_var = "method",
  title = "OBD Selection Rate Comparison",
  y_label = "OBD Selection (%)",
  limits = c(0, 100),
  file_path = "results/plots/obd_selection_comparison.png"
)

Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
ℹ Please use tidy evaluation idioms with `aes()`.
ℹ See also `vignette("ggplot2-in-packages")` for more information.

print(p_obd)

# Sample Size Comparison
sample_data <- expand.grid(
  scenario = scenarios,
  method = methods,
  stringsAsFactors = FALSE
)
sample_data$avg_n <- c(25, 20, 30, 22, 18, 28, 18, 15, 25)

# Create sample size plot
p_sample <- plot_method_comparison_bars(
  sample_data,
  x_var = "scenario", y_var = "avg_n", fill_var = "method",
  title = "Average Sample Size Comparison",
  y_label = "Average Sample Size",
  limits = c(0, 35),
  file_path = "results/plots/sample_size_comparison.png"
)
print(p_sample)

# Safety (Overdose) Comparison
safety_data <- expand.grid(
  scenario = scenarios,
  method = methods,
  stringsAsFactors = FALSE
)
safety_data$overdose_pct <- c(15, 10, 20, 12, 8, 18, 8, 5, 15)

# Create safety plot
p_safety <- plot_method_comparison_bars(
  safety_data,
  x_var = "scenario", y_var = "overdose_pct", fill_var = "method",
  title = "Overdose Patient Percentage",
  y_label = "Overdose Pts (%)",
  limits = c(0, 25),
  file_path = "results/plots/safety_comparison.png"
)
print(p_safety)

cat("✅ Method comparison plots created successfully!\n")

✅ Method comparison plots created successfully!

cat("📁 All plots saved to results/plots/ directory\n")

📁 All plots saved to results/plots/ directory

Multi-Scenario Analysis

This section creates multi-scenario dose-response curves similar to the reference code.

# Create multi-scenario analysis
cat("\n=== Creating Multi-Scenario Analysis ===\n")

=== Creating Multi-Scenario Analysis ===

# Define different scenarios with varying parameters
scenarios_data <- list(
  list(
    toxicity = c(0.1, 0.18, 0.35, 0.40, 0.50),
    efficacy = c(0.35, 0.35, 0.37, 0.39, 0.39),
    utility = c(0.27, 0.23, 0.10, 0.13, 0.17)
  ),
  list(
    toxicity = c(0.05, 0.15, 0.25, 0.35, 0.50),
    efficacy = c(0.10, 0.35, 0.35, 0.38, 0.39),
    utility = c(0.07, 0.22, 0.22, 0.12, 0.06)
  ),
  list(
    toxicity = c(0.02, 0.06, 0.10, 0.20, 0.35),
    efficacy = c(0.05, 0.10, 0.35, 0.35, 0.40),
    utility = c(0.03, 0.07, 0.28, 0.22, 0.13)
  )
)

# Create multi-scenario plot
multi_scenario_plot <- plot_multi_scenario_curves(
  scenarios_data,
  title = "Dose-Response Curves Across Scenarios",
  file_path = "results/plots/multi_scenario_analysis.png"
)

Scale for y is already present.
Adding another scale for y, which will replace the existing scale.

print(multi_scenario_plot)

cat("✅ Multi-scenario analysis completed!\n")

✅ Multi-scenario analysis completed!

======= Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.7 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- PoC detection rate = 0.000 (95% CI: [0.000, 0.036]) Progress: 2/6 - Testing C_poc = 0.750 --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.75 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- PoC detection rate = 0.000 (95% CI: [0.000, 0.036]) Progress: 3/6 - Testing C_poc = 0.800 --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.8 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- PoC detection rate = 0.000 (95% CI: [0.000, 0.036]) Progress: 4/6 - Testing C_poc = 0.850 --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.85 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- PoC detection rate = 0.000 (95% CI: [0.000, 0.036]) Progress: 5/6 - Testing C_poc = 0.900 --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.9 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- PoC detection rate = 0.000 (95% CI: [0.000, 0.036]) Progress: 6/6 - Testing C_poc = 0.950 --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- --- Stage 1 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.235 0.322 0.428 Summary: Efficacy marginal means: 0.556 0.629 0.664 Summary: Immune response means: 0.285 0.305 0.357 Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.285 Toxicity given I=0 (π_T|I=0): 0.194 Toxicity given I=1 (π_T|I=1): 0.335 Efficacy given I=0 (π_E|I=0): 0.531 Efficacy given I=1 (π_E|I=1): 0.62 Probability distributions: P(T=0|I=0): 0.806 P(T=1|I=0): 0.194 P(T=0|I=1): 0.665 P(T=1|I=1): 0.335 P(E=0|I=0): 0.469 P(E=1|I=0): 0.531 P(E=0|I=1): 0.38 P(E=1|I=1): 0.62 Expected utility given I=0: 37.35 Expected utility given I=1: 52.03 Total expected utility: 41.54 Dose 2 Utility Calculation: Immune response probability (π_I): 0.305 Toxicity given I=0 (π_T|I=0): 0.247 Toxicity given I=1 (π_T|I=1): 0.496 Efficacy given I=0 (π_E|I=0): 0.615 Efficacy given I=1 (π_E|I=1): 0.662 Probability distributions: P(T=0|I=0): 0.753 P(T=1|I=0): 0.247 P(T=0|I=1): 0.504 P(T=1|I=1): 0.496 P(E=0|I=0): 0.385 P(E=1|I=0): 0.615 P(E=0|I=1): 0.338 P(E=1|I=1): 0.662 Expected utility given I=0: 41.58 Expected utility given I=1: 48.22 Total expected utility: 43.61 Dose 3 Utility Calculation: Immune response probability (π_I): 0.357 Toxicity given I=0 (π_T|I=0): 0.32 Toxicity given I=1 (π_T|I=1): 0.626 Efficacy given I=0 (π_E|I=0): 0.634 Efficacy given I=1 (π_E|I=1): 0.717 Probability distributions: P(T=0|I=0): 0.68 P(T=1|I=0): 0.32 P(T=0|I=1): 0.374 P(T=1|I=1): 0.626 P(E=0|I=0): 0.366 P(E=1|I=0): 0.634 P(E=0|I=1): 0.283 P(E=1|I=1): 0.717 Expected utility given I=0: 40.58 Expected utility given I=1: 45.83 Total expected utility: 42.46 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5 2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6 3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 1 0 0 --- Stage 2 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.143 0.291 0.416 Summary: Efficacy marginal means: 0.644 0.675 0.699 Summary: Immune response means: 0.237 0.276 0.344 Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 1 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.237 Toxicity given I=0 (π_T|I=0): 0.109 Toxicity given I=1 (π_T|I=1): 0.255 Efficacy given I=0 (π_E|I=0): 0.632 Efficacy given I=1 (π_E|I=1): 0.688 Probability distributions: P(T=0|I=0): 0.891 P(T=1|I=0): 0.109 P(T=0|I=1): 0.745 P(T=1|I=1): 0.255 P(E=0|I=0): 0.368 P(E=1|I=0): 0.632 P(E=0|I=1): 0.312 P(E=1|I=1): 0.688 Expected utility given I=0: 47.08 Expected utility given I=1: 60.58 Total expected utility: 50.27 Dose 2 Utility Calculation: Immune response probability (π_I): 0.276 Toxicity given I=0 (π_T|I=0): 0.218 Toxicity given I=1 (π_T|I=1): 0.483 Efficacy given I=0 (π_E|I=0): 0.663 Efficacy given I=1 (π_E|I=1): 0.706 Probability distributions: P(T=0|I=0): 0.782 P(T=1|I=0): 0.218 P(T=0|I=1): 0.517 P(T=1|I=1): 0.483 P(E=0|I=0): 0.337 P(E=1|I=0): 0.663 P(E=0|I=1): 0.294 P(E=1|I=1): 0.706 Expected utility given I=0: 45.79 Expected utility given I=1: 51.67 Total expected utility: 47.42 Dose 3 Utility Calculation: Immune response probability (π_I): 0.344 Toxicity given I=0 (π_T|I=0): 0.309 Toxicity given I=1 (π_T|I=1): 0.62 Efficacy given I=0 (π_E|I=0): 0.676 Efficacy given I=1 (π_E|I=1): 0.744 Probability distributions: P(T=0|I=0): 0.691 P(T=1|I=0): 0.309 P(T=0|I=1): 0.38 P(T=1|I=1): 0.62 P(E=0|I=0): 0.324 P(E=1|I=0): 0.676 P(E=0|I=1): 0.256 P(E=1|I=1): 0.744 Expected utility given I=0: 43.64 Expected utility given I=1: 47.71 Total expected utility: 45.04 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3 2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4 3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0 --- End Utility Calculations --- Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores) Allocation probabilities for next stage: 0.5146174 0.4853826 0 --- Stage 3 --- Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+) Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities) --- Admissibility Check --- Summary: Toxicity marginal means: 0.109 0.22 0.391 Summary: Efficacy marginal means: 0.694 0.709 0.725 Summary: Immune response means: 0.204 0.219 0.316 Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 ) Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 ) Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 ) --- End Admissibility Check --- Admissible set: 2 Workflow: Step 4 - Early Termination Check --- Utility Score Calculations --- Utility Table Reference: I=0 (No Immune Response): E=0, T=0: 0 E=1, T=0: 80 E=0, T=1: 0 E=1, T=1: 30 I=1 (Immune Response): E=0, T=0: 10 E=1, T=0: 100 E=0, T=1: 0 E=1, T=1: 40 Dose 1 Utility Calculation: Immune response probability (π_I): 0.204 Toxicity given I=0 (π_T|I=0): 0.083 Toxicity given I=1 (π_T|I=1): 0.207 Efficacy given I=0 (π_E|I=0): 0.684 Efficacy given I=1 (π_E|I=1): 0.733 Probability distributions: P(T=0|I=0): 0.917 P(T=1|I=0): 0.083 P(T=0|I=1): 0.793 P(T=1|I=1): 0.207 P(E=0|I=0): 0.316 P(E=1|I=0): 0.684 P(E=0|I=1): 0.267 P(E=1|I=1): 0.733 Expected utility given I=0: 51.84 Expected utility given I=1: 66.29 Total expected utility: 54.79 Dose 2 Utility Calculation: Immune response probability (π_I): 0.219 Toxicity given I=0 (π_T|I=0): 0.151 Toxicity given I=1 (π_T|I=1): 0.469 Efficacy given I=0 (π_E|I=0): 0.699 Efficacy given I=1 (π_E|I=1): 0.741 Probability distributions: P(T=0|I=0): 0.849 P(T=1|I=0): 0.151 P(T=0|I=1): 0.531 P(T=1|I=1): 0.469 P(E=0|I=0): 0.301 P(E=1|I=0): 0.699 P(E=0|I=1): 0.259 P(E=1|I=1): 0.741 Expected utility given I=0: 50.63 Expected utility given I=1: 54.65 Total expected utility: 51.51 Dose 3 Utility Calculation: Immune response probability (π_I): 0.316 Toxicity given I=0 (π_T|I=0): 0.287 Toxicity given I=1 (π_T|I=1): 0.609 Efficacy given I=0 (π_E|I=0): 0.706 Efficacy given I=1 (π_E|I=1): 0.768 Probability distributions: P(T=0|I=0): 0.713 P(T=1|I=0): 0.287 P(T=0|I=1): 0.391 P(T=1|I=1): 0.609 P(E=0|I=0): 0.294 P(E=1|I=0): 0.706 P(E=0|I=1): 0.232 P(E=1|I=1): 0.768 Expected utility given I=0: 46.36 Expected utility given I=1: 49.63 Total expected utility: 47.4 Utility Summary Table: Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U -----|--------|----------|----------|----------|----------|--------|--------|-------- 1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8 2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5 3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4 --- End Utility Calculations --- Workflow: Step 5 - Final Selection with PoC validation PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000 --- PoC THRESHOLD CHECK --- Maximum PoC probability: 0 PoC threshold: 0.95 PoC threshold met: FALSE --- END PoC CHECK --- --- FINAL DOSE SELECTION WITH PoC --- Admissible doses: 2 Utilities: 51.51 Selected dose: 2 Selected utility: 51.51 PoC validated: FALSE Max PoC probability: 0 Selection reason: PoC threshold not met, but selecting best available dose --- END FINAL SELECTION --- PoC detection rate = 0.000 (95% CI: [0.000, 0.036]) === CALIBRATION COMPLETE === Optimal C_poc = 0.700 Achieved detection rate = 0.000 (target: 0.100) Difference from target = 0.100 ============================